U.S. patent application number 14/904890 was filed with the patent office on 2016-06-09 for method and device for measuring displacement distribution of an object using repeated pattern, and program for the same.
This patent application is currently assigned to NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY. The applicant listed for this patent is NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY. Invention is credited to Shien RI, Hiroshi TSUDA.
Application Number | 20160161249 14/904890 |
Document ID | / |
Family ID | 52345891 |
Filed Date | 2016-06-09 |
United States Patent
Application |
20160161249 |
Kind Code |
A1 |
RI; Shien ; et al. |
June 9, 2016 |
METHOD AND DEVICE FOR MEASURING DISPLACEMENT DISTRIBUTION OF AN
OBJECT USING REPEATED PATTERN, AND PROGRAM FOR THE SAME
Abstract
In the present invention, conventional problems that the scheme
is not suitable for nano/micro materials or large structures, and
that if the scheme is applied to a regular pattern with two or more
cycles of arbitrary repetition, a large error is generated are
solved by using a higher order frequency of moire fringes generated
using an arbitrary regular pattern having one-dimensional or
two-dimensional repetition artificially produced on a surface of an
object or previously present on the surface of the object, or phase
information in a plurality of frequency components, and improvement
of measurement precision and a dramatic increase in a limit of a
measurement scale are achieved.
Inventors: |
RI; Shien; (Tsukuba-shi,
JP) ; TSUDA; Hiroshi; (Tsukuba-shi, JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND
TECHNOLOGY |
Tokyo |
|
JP |
|
|
Assignee: |
NATIONAL INSTITUTE OF ADVANCED
INDUSTRIAL SCIENCE AND TECHNOLOGY
Chiyoda-ku, Tokyo
JP
|
Family ID: |
52345891 |
Appl. No.: |
14/904890 |
Filed: |
December 5, 2013 |
PCT Filed: |
December 5, 2013 |
PCT NO: |
PCT/JP2013/082701 |
371 Date: |
January 13, 2016 |
Current U.S.
Class: |
702/42 |
Current CPC
Class: |
G01B 11/165 20130101;
G01M 5/0041 20130101; G01B 11/16 20130101; G01M 5/0091 20130101;
G01M 5/0058 20130101; G01N 3/068 20130101 |
International
Class: |
G01B 11/16 20060101
G01B011/16; G01M 5/00 20060101 G01M005/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 18, 2013 |
JP |
2013-149340 |
Claims
1. A method for measuring displacement distribution of an object by
capturing a digital image before and after deformation of a regular
pattern such as a sine wave or a rectangular wave grating being
affixed to an object surface and having repetition according to
desired measurement precision in intensity distribution in a
horizontal direction or a vertical direction with an equal spacing
pitch or a regular pattern such as vertical or horizontal fringe
pattern appearing on an outer wall surface that is a structure of
the object presenting on the object surface and having repetition
in which a suitable precision in measurement can be expected in the
intensity distribution in the horizontal direction or the vertical
direction with an equal spacing pitch using an optical camera, and
processing the digital image in a displacement distribution
measurement device, the method comprising steps of: acquiring a
pattern image before and after the deformation; performing a
thin-out process and intensity interpolation at arbitrary fixed
sampling intervals which is equivalent to an analysis frequency and
may not match a pitch of the regular pattern in the horizontal
direction or the vertical direction on intensity data of the
pattern image, and generating a plurality of moire fringe images
with a low spatial frequency of which the phase is shifted;
performing a Fourier transform on a moire fringe image of which the
phase is shifted, extracting information on a specific frequency
component such as a component with maximum amplitude or power
corresponding to the analysis frequency, and obtaining phase
distribution of moire fringe images of a fundamental frequency in
which the analysis frequency and the pitch of the regular pattern
are assumed not to match each other or a higher order frequency in
the horizontal direction or the vertical direction; and calculating
the displacement distribution of the object from phase difference
distribution obtained from phase distributions of the moire fringes
before and after the deformation, wherein an equation for obtaining
a displacement distribution u from the phase difference
distribution at the specific frequency .omega. of the moire fringes
is shown as; [Equation 1] [ Equation 7 ] u ( i , j ; .omega. ) = -
p 2 .pi. .omega. .DELTA. .phi. M ( i , j ; .omega. ) ( 7 )
##EQU00007## in which i and j denote a horizontal coordinate and a
vertical coordinate of the captured image, p denotes an actual
value of a pitch spacing of the regular pattern in the horizontal
direction or the vertical direction, M denotes the analysis
frequency, .omega. denotes the fundamental frequency in which the
analysis frequency and the pitch of the regular pattern are assumed
not to match each other or the higher order frequency, and .phi.
denotes a phase distribution function.
2. A method for measuring displacement distribution of an object by
capturing a digital image before and after deformation of a
one-dimensional regular pattern such as a tile pattern of an
external wall that is a structure of an object or a window pattern
of a high-rise building having two or more cycles of repetition
with an equal spacing pitch in a horizontal direction and a
vertical direction present or affixed on a surface of an object
using an optical camera, and processing the digital image in a
displacement distribution measurement device, the method comprising
steps of: acquiring a one-dimensional regular pattern image before
and after the deformation; performing a thin-out process and
intensity interpolation at arbitrary fixed sampling intervals which
is equivalent to an analysis frequency and may not match a pitch of
the regular pattern in the horizontal direction or the vertical
direction on intensity data of the one-dimensional regular pattern
image to generate a plurality of moire fringe images of which the
phase is shifted; performing a Fourier transform on the moire
fringe image of which the phase is shifted, simultaneously
extracting information on a plurality of a frequency components
corresponding to the analysis frequency, and obtaining phase
distribution of the moire fringe image of a plurality of
frequencies in the horizontal direction or the vertical direction;
and performing weighting with amplitude or power at each frequency
and combination based on a plurality of phase difference
distributions obtained from phase distribution of the moire fringes
before and after the deformation, and calculating the displacement
distribution of the object with a small measurement error for a
predetermined repetitive pattern.
3. A method for measuring displacement distribution of an object by
capturing a digital image before and after deformation of a
two-dimensional regular pattern such as an arbitrary pattern of an
alphanumeric character or a floral pattern in which the same
pattern has two or more repetitions with an equal spacing pitch in
a horizontal direction or a vertical direction present or affixed
on a surface of an object using an optical camera, and processing
the digital image in a displacement distribution measurement
device, the method comprising steps of: acquiring a two-dimensional
regular pattern image before and after the deformation; performing
a thin-out process and intensity interpolation at arbitrary fixed
sampling intervals which is equivalent to an analysis frequency and
may not match a pitch of the regular pattern in the horizontal
direction or the vertical direction on intensity data of the
two-dimensional regular pattern image to generate a plurality of
moire fringe images of which the phase is shifted; performing a
Fourier transform on the moire fringe image of which the phase is
shifted, simultaneously extracting information on a plurality of a
frequency components corresponding to the analysis frequency, and
obtaining phase distribution of the moire fringe image of a
plurality of frequencies in the horizontal direction or the
vertical direction; and performing weighting with amplitude or
power at each frequency and combination based on a plurality of
phase difference distributions obtained from phase distribution of
the moire fringes before and after the deformation, and calculating
the displacement distribution of the object with a small
measurement error for a predetermined repetitive pattern.
4. A method for measuring displacement distribution of an object by
capturing a digital image before and after deformation of a regular
pattern with repetition in which desired measurement precision is
able to be expected in intensity distribution at least in a
horizontal direction or a vertical direction with an equal spacing
pitch present or affixed on the surface of the object using an
optical camera, and processing the digital image in a displacement
distribution measurement device, the method comprising steps of:
acquiring a regular pattern image before and after the deformation;
performing a thin-out process and intensity interpolation at
arbitrary fixed sampling intervals which is equivalent to an
analysis frequency and may not match a pitch of the regular pattern
in the horizontal direction or the vertical direction on intensity
data of the regular pattern image to generate a plurality of moire
fringe images of which the phase is shifted; performing Fourier
transform on the moire fringe image of which the phase is shifted,
simultaneously extracting information on a plurality of a frequency
components corresponding to the analysis frequency, and obtaining
phase distribution of the moire fringe image of a plurality of
frequencies in the horizontal direction or the vertical direction;
and performing weighting with amplitude or power at each frequency
and combination based on a plurality of phase difference
distributions obtained from phase distribution of the moire fringes
before and after the deformation, and calculating the displacement
distribution of the object with a small measurement error for a
predetermined repetitive pattern.
5. A computer-readable recording medium having a program recorded
thereon, wherein steps according to claim 1 are executed in an
object displacement distribution analysis program.
6. A computer-readable recording medium having a program recorded
thereon, wherein steps according to claim 2 are executed in an
object displacement distribution analysis program.
7. A computer-readable recording medium having a program recorded
thereon, wherein steps according to claim 3 are executed in an
object displacement distribution analysis program.
8. A computer-readable recording medium having a program recorded
thereon, wherein steps according to claim 4 are executed in an
object displacement distribution analysis program.
9. A device for measuring displacement distribution of an object,
wherein the device measures displacement distribution of the object
by performing the method according to claim 1.
10. A device for measuring displacement distribution of an object,
wherein the device measures displacement distribution of the object
by performing the method according to claim 2.
11. A device for measuring displacement distribution of an object,
wherein the device measures displacement distribution of the object
by performing the method according to claim 3.
12. A device for measuring displacement distribution of an object,
wherein the device measures displacement distribution of the object
by performing the method according to claim 4.
Description
TECHNICAL FIELD
[0001] The present invention relates to an analysis method, device,
and program capable of easily measuring the displacement
distribution of an object with high resolution, with high
precision, and at a high speed from a regular pattern with
arbitrary repetition on the object captured by an optical
camera.
BACKGROUND ART
[0002] Technology for measuring displacement distribution of a
structure has been widely available from evaluation of the
mechanical characteristics of a nano/micro material to evaluation
of the health monitoring of a large infrastructure.
[0003] A mechanical contact displacement gauge or a non-contact
type laser displacement gauge is often used, but only displacement
information of one point and one direction is obtained and the
displacement gauge is not suitable for recognition of the
displacement behavior of an entire structure.
[0004] Therefore, a displacement distribution (full-field)
measurement method in which displacement distribution in an image
captured using an optical camera is obtained is effective.
[0005] As a method of displacement distribution measurement using a
digital image, there is a digital image correlation (DIC) method,
which is currently utilized in many fields.
[0006] This DIC method is characterized by use of a random pattern
having no regularity.
[0007] On the other hand, a method of measuring a small amount of
displacement distribution intentionally using a grating pattern
with regularity in idea of reversal has also been proposed, as
described in Patent Literature 1.
CITATION LIST
Patent Literature
[0008] [Patent Literature 1] Japanese Patent No. 4831703 Non-Patent
Literature [0009] [Non-Patent Literature 1] Chu, T. C., Ranson, W.
F. Sutton, M. A. and Peters, W. H., applications of
Digital-Image-Correlation Techniques to Experimental Mechanics,
Experimental Mechanics, Vol. 25, No. 3 (1985), pp. 232-244.
SUMMARY OF INVENTION
Technical Problem
[0010] A conventional displacement distribution measurement method
using a digital image includes a digital image correlation method
using a random pattern often present on a surface of a target or is
intentionally painted.
[0011] In a displacement distribution measurement technology
described in Non-Patent Literature 1, an amount of deformation is
calculated by obtaining a correlation of a certain evaluation area
(i.e., subset) for a random pattern before and after deformation.
However, a large calculation time is required in the case of a
high-resolution image.
[0012] Further, precision of measurement is limited from 1/20
pixels to 1/50 pixels. Further, it is technically difficult for a
target of a nano/micro scale to be painted with any random pattern.
There are problems in that it is not easy for a target of a mega
scale of a few meters or more to be painted with a random pattern,
and time and resources are required. In addition, this is not
preferable in terms of (beauty) appearance.
[0013] On the other hand, a sampling moire method (Patent
Literature 1) capable of measuring a small displacement
distribution by generating moire fringes for a fringe image
captured by a digital camera using a fringe pattern with regularity
and calculating phase information of the moire fringes has been
developed.
[0014] With this measurement technology, a small displacement
distribution can be measured with precision of 1/1000 of a grating
pitch affixed to a structure surface. However, a grating used for
measurement is a sine wave (or cosine wave) or a rectangular wave
pattern in which a white-to-black ratio is 1:1. When a nano/micro
material or a large structure is a target, such a pattern is not
necessarily affixed to a structure surface and an application is
limited. Further, when technology is applied to a regular pattern
with two or more cycles of arbitrary repetition, a conventional
analysis method has a problem in that a large amount of error is
generated.
Solution to Problem
[0015] In order to solve the above problems, the present invention
is intended to easily measure displacement distribution, with high
precision, and at a high speed using a regular pattern present on a
structure surface from a nano scale to a mega scale as shown in
FIG. 1. According to a form of a regular pattern image to be
analyzed, two displacement distribution measurement methods are
considered. Hereinafter, each measurement method will be
described.
[0016] FIG. 1 shows an example of a pattern having applicable
regularity in the present invention, and is not intended to limit
the regular pattern.
[0017] Further, two methods to be described next are methods
suitable for a regular pattern of an object that is a target, but
each regular pattern is not limited to the illustrated regular
pattern.
[0018] (1) Displacement distribution analysis method 1:
Displacement distribution analysis method based on an arbitrary
analysis pitch using a single higher order frequency
[0019] In the present invention, moire fringes are generated based
on image data of a one-dimensional regular pattern with repetition
with an equal spacing pitch, which is artificially produced on an
object surface (for example, affixing of a grating pattern or
transferring of the pattern) or previously present on the object
surface, and displacement distribution is measured based on phase
information on a specific higher order frequency.
[0020] This displacement distribution analysis method capable of
easily performing higher speed processing can be suitably applied
to, more particularly, a regular pattern (for example, a sine wave
lattice or a rectangular wave grating that is affixed) having
repetition according to a suitable accuracy in measurement in
intensity distribution in a horizontal direction or a vertical
direction with an equal spacing pitch affixed to the object surface
or a regular pattern (for example, vertical or horizontal fringe
pattern appearing on an outer wall surface that is a structure of
the object) having repetition in which a suitable accuracy in
measurement can be expected in the intensity distribution in the
horizontal direction or the vertical direction with an equal
spacing pitch (p) present on the object surface.
[0021] The regular patterns described above are examples of the
regular pattern and is not intended to limit an applicable regular
pattern of the present invention.
[0022] FIG. 2 shows a principle of displacement distribution
analysis using an arbitrary analysis pitch that is first method
(1), and an image processing method. When a pattern having
regularity according to a suitable accuracy in measurement in
intensity distribution in a horizontal direction or a vertical
direction with an equal spacing pitch affixed to a measurement
target surface, such as a sine wave or rectangular wave fringe
pattern, is captured by an optical camera, one fringe pattern image
having a intensity distribution as expressed by Equation 1 in an
approximate manner is obtained.
[ Equation 1 ] f ( i , j ) = a cos { 2 .pi. i P + .phi. 0 ( i , j )
} + b = a cos { .phi. ( i , j ) } + b ( 1 ) ##EQU00001##
[0023] Here, f(i, j) denotes an intensity value (brightness) on
coordinates (i, j) of a captured image, a denotes an amplitude of
the fringe pattern, b denotes background intensity, .phi..sub.0
denotes an initial phase of the fringe pattern, and .phi. is an
obtained phase value of the fringe pattern. Further, P denotes a
grating pitch spacing in an i-direction on the captured image.
[0024] M moire fringe images of which the phase has been shifted
are obtained through a process of performing an image thin-out
process on one captured fringe grating image while changing, pixel
by pixel, a start point m of the decimation for the i-direction at
an arbitrary pitch spacing M (which is generally an integer) and
performing intensity interpolation using an intensity value of an
adjacent image.
[ Equation 2 ] f M ( i , j ; m ) = a cos { 2 .pi. ( 1 P - 1 M ) i +
.phi. 0 ( i , j ) + 2 .pi. m M } + b = a cos { .phi. M ( i , j ) +
2 .pi. m M } + b ( 2 ) ##EQU00002##
[0025] While the image processing method such as a thin-out process
and intensity interpolation described above are the same as that
described in Patent Literature 1, a key point is that it is not
necessary for the analysis pitch (M; regularity pitch on the image
data) to match the pitch spacing (P; equal spacing pitch) of the
lattice pattern, and analysis can be performed at arbitrary
decimation spacing.
[0026] Further, this key point applies to second method.
[0027] If discrete Fourier transform shown in Equation 3 is applied
to the plurality of moire fringes obtained through the thin-out and
the intensity interpolation, phase distribution .phi..sub.M(i,j;
.omega.) at an arbitrary frequency component (.omega.) of the moire
fringes can be obtained.
[ Equation 3 ] .phi. M ( i , j ; .omega. ) = - arc tan m = 0 M - 1
f M ( i , j ; m ) sin .omega. ( 2 .pi. m M ) m = 0 M - 1 f M ( i ,
j ; m ) cos .omega. ( 2 .pi. m M ) ( 3 ) ##EQU00003##
[0028] The same image processing can be performed on the pattern
after deformation to similarly obtain phase distribution
.phi.'.sub.M(i,j; .omega.) at an arbitrary frequency component of
the moire fringes after deformation. Finally, as shown in Equation
4, displacement distribution u(i, j; .omega.) in an x-direction can
be calculated from a phase difference
.DELTA..phi..sub.M=.phi.'.sub.M-.phi..sub.M of the moire fringes
before and after deformation.
[ Equation 4 ] u ( i , j ; .omega. ) = - p 2 .pi. .omega. .DELTA.
.phi. M ( i , j ; .omega. ) ( 4 ) ##EQU00004##
[0029] Similarly, when the above-described image processing is
performed with respect to y-direction, displacement distribution
v(i, j; .omega.) in the y-direction can be obtained.
[0030] (2) Displacement distribution analysis scheme 2: Method of
analyzing displacement distribution using an arbitrary regular
pattern using a plurality of frequency components
[0031] FIG. 3 shows a principle of displacement distribution
analysis using arbitrary regular patterns seen in daily life and an
image processing method, which is second method (2).
[0032] In these regular patterns, the regularity of the patterns is
seen differently during visual observation. Accordingly, the
regular patterns can be roughly classified into a one-dimensional
regular pattern (for example, a tile pattern of an external wall
that is a structure of an object or a window pattern of a high-rise
building) having two or more cycles of repetition with an equal
spacing pitch in a horizontal direction and a vertical direction,
which is present or affixed to a surface of an object, and a
two-dimensional regular pattern (for example, an arbitrary pattern
such as an alphanumeric character or a floral pattern) in which the
same pattern has two or more repetitions with an equal spacing
pitch in a horizontal direction or a vertical direction, which is
present or affixed to a surface of an object, but appropriate
processing for image data which is intensity distribution data
thereof is the same.
[0033] Further, the arbitrary regular pattern seen in daily life
described above may refer to a regular pattern with repetition in
which a suitable precision in measurement can be expected in
intensity distribution at least in a horizontal direction or a
vertical direction with an equal spacing pitch, which is present or
affixed to the surface of the object.
[0034] If the regular pattern having an arbitrary repetition on a
measurement target surface is captured by an optical camera, one
fringe pattern image having intensity distribution as expressed by
Equation 5 is obtained. This is because an arbitrary regular
pattern can be expressed by a plurality of Fourier series including
a higher order frequency.
[ Equation 5 ] g ( i , j ) = .omega. = 1 W a .omega. cos .omega. {
2 .pi. i P + .phi. 0 ( i , j ) } + b = .omega. = 1 W a .omega. cos
.omega. { .phi. ( i , j ) } + b ( 5 ) ##EQU00005##
[0035] Here, g(i, j) denotes a intensity value (brightness) on a
coordinates (i, j) of a captured image of an arbitrary regular
pattern. W denotes an order of a higher order frequency,
a.sub..omega. denotes (a plurality of) amplitudes of the fringe
lattice at each frequency, b denotes background intensity,
.phi..sub.0 denotes an initial phase of the fringe pattern, and
.phi. denotes an obtained phase value of the fringe pattern.
Further, P denotes a grating pitch spacing in the i-direction on
the captured image.
[0036] M moire fringe images of which the phase has been shifted
are obtained through a process of performing an image thin-out
process on one captured fringe pattern image while changing, pixel
by pixel, a start point m of the thin-out for the i-direction at an
arbitrary pitch spacing M (which is generally an integer) and
performing intensity interpolation using an intensity values of an
adjacent image.
[ Equation 6 ] g M ( i , j ; m ) = .omega. = 1 W a .omega. cos { 2
.pi. ( 1 P - 1 M ) i + .phi. 0 ( i , j ) + 2 .pi. m M } + b =
.omega. = 1 W a .omega. cos { .phi. M ( i , j ) + 2 .pi. m M } + b
, ( m = 0 , 1 , , M - 1 ) ( 6 ) ##EQU00006##
[0037] Since Moire is a kind of enlargement phenomenon, moire
fringes having a low spatial frequency obtained here are also
regular, and can be represented by Fourier series including a
higher order frequency, as shown in Equation 6.
[0038] In the present invention, a plurality of frequency
components are simultaneously extracted using this property.
Amplitude information (or power spectrum information) and phase
information of a plurality of frequency components are
simultaneously calculated using discrete Fourier transform.
[0039] Similarly, the regular pattern after object deformation is
captured, the thin-out process and the intensity interpolation are
performed, and phase information of the plurality of frequency
components of moire fringes after deformation are simultaneously
calculated through Fourier transform.
[0040] A plurality of displacement distributions u(i, j; .omega.)
in the x-direction can be calculated from the phase difference of
the plurality of respective frequencies of the moire fringes before
and after deformation using Equation 4. Weighting is performed with
obtained final amplitude or power at each frequency and combination
is performed so as to obtain final displacement distribution u(i,
j).
[0041] According to the above method, since a higher order
frequency component, as well as a component of frequency 1 that is
a fundamental frequency, is considered, it is possible to cope with
an arbitrary regular pattern and perform highly accurate
displacement distribution measurement with less measurement
error.
[0042] Similarly, by performing the above-described image
processing with respect to a the y-direction, it is possible to
obtain the displacement distribution v(i, j) in the
y-direction.
Advantageous Effects of Invention
[0043] According to the present invention, if there is a regular
pattern with an arbitrary repetition on a surface of a measurement
target, it is possible to analyze the displacement distribution
easily, with high precision, and at high speed.
[0044] As effect 1, it is not necessary to limit the spacing of
analysis pitches for the regular pattern, and it is possible to
obtain the displacement distribution more easily, with high
precision, and at high speed.
[0045] As effect 2, since the present invention can be applied to
the regular pattern having an arbitrary repetition, an applicable
range is wide.
BRIEF DESCRIPTION OF DRAWINGS
[0046] FIG. 1 is a diagram illustrating a regular pattern to which
the present invention can be applied.
[0047] FIG. 2 is a diagram illustrating a principle of displacement
distribution measurement based on an arbitrary analysis pitch for a
regular pattern.
[0048] FIG. 3 is a diagram illustrating a principle of displacement
distribution measurement that uses a regular pattern with arbitrary
repetition.
[0049] FIG. 4 is a photograph of a 3-point bending experiment
apparatus for small deflection distribution measurement of a metal
material.
[0050] FIG. 5 is a diagram illustrating experimental results of
small deflection distribution measurement of a metal material.
[0051] FIG. 6 is a diagram illustrating comparison of measurement
precision when a one-dimensional regular pattern is used through
simulation.
[0052] FIG. 7 is a diagram illustrating a simulation result of a
relationship between an order of an analysis frequency and a
measurement error.
[0053] FIG. 8 is a diagram illustrating an optical system for
displacement measurement using a one-dimensional regular
pattern.
[0054] FIG. 9 is a diagram illustrating an experimental result of
the displacement measurement using the one-dimensional regular
pattern.
[0055] FIG. 10 is a diagram illustrating an optical system for
displacement measurement using a two-dimensional regular
pattern.
[0056] FIG. 11 is a diagram illustrating an experimental result of
the displacement measurement using the two-dimensional regular
pattern.
DESCRIPTION OF EMBODIMENTS
[0057] Hereinafter, embodiments of the present invention will be
described with reference to the accompanying drawings.
Example 1
Improvement of Measurement Precision of Displacement Distribution
Based on Single Higher Order Frequency
[0058] Experimental results of a metal material 3-point bending
test for verifying improvement of displacement measurement
precision according to an arbitrary frequency component based on
first method (1) of the present invention are shown below. FIG. 4
shows an optical system for the experiment. In this experiment,
after a sine wave grating having a pitch spacing of 1.13 mm was
affixed to a surface of an aluminum bar having a size of
360.times.12.times.12 mm, a load of 9.8 N (1 kg) and 19.6 N (2 kg)
was loaded at a center position of which the fulcrum distance was
250 mm, and respective grating images before and after deformation
were captured by a general-purpose CCD camera. A camera was
installed so that one cycle of the grating pitch is 5 pixels on the
captured image.
[0059] For the same grating images, deflection distributions
obtained by a conventional measurement method (analysis in which a
sampling pitch is 5 pixels) and the measurement method of the
present invention (analysis in which the sampling pitch is 15
pixels) are compared so as to confirm the validity of the present
invention.
[0060] FIG. 5(a) shows a Fourier spectrum distribution in a center
pixel near a load point. In the conventional method, since an
analysis is performed in which the sampling pitch is about the same
width of five pixels that are substantially the same as the grating
pitch, large amplitude appears in a component of frequency 1, as
shown in FIG. 5(a).
[0061] Meanwhile, in the method using the method (1) of the present
invention, since the sampling pitch is expanded to three cycles so
at to perform analysis, large amplitude appears in a component of
frequency 3, as shown in FIG. 5(b).
[0062] FIGS. 5(c) and 5(d) show deflection distribution of a
horizontal center line measured using the conventional method and
the present invention. FIG. 5(c) shows a result of analysis using
fundamental frequency 1 in a conventional method, and FIG. 5(d)
shows a result of analysis using frequency 3 according to the
present invention.
[0063] According to the present invention, it was confirmed that
the variation of measurement due to random noise of the CCD camera
was reduced, and displacement (deflection) distribution with less
variation was obtained.
Example 2
Verification of Improvement of Displacement Distribution
Measurement Precision of Regular Pattern Through Simulation
[0064] Effects thereof were confirmed through simulation in order
to confirm effectiveness of the method described in the second
method (2) of the present invention.
[0065] Here, two types of tile patterns of 20 pixels of one cycle
(regarded as a grating pitch of 1 mm) in which white is brightness
1 and black is brightness 0 were produced. One of the tile patterns
was a tile pattern in which there were 2 white pixels and 18 black
pixels among the 20 pixels, and a white-to-black ratio was 1:9. The
other was a tile pattern in which there was 1 white pixel and 19
black pixels, and a white-to-black ratio was 1:19. A measurement
error when displacement is imparted to two types of grating images
by 0.05 mm from 0 mm to 1 mm on a computer was investigated.
[0066] Analysis of an amount of displacement was performed in a
state in which random noise of 10% was applied to a tile pattern
image at each position in consideration of noise generated in
elements of a digital camera at the time of actual measurement. In
the analysis, a thin-out number (sampling pitch) was set to 20
pixels, and a result of analyzing only frequency 1 described in
Patent Literature 1 of the related art and a result of analysis in
consideration fundamental frequency component and first to fifth
order frequency components according to the present invention were
compared.
[0067] FIG. 6 shows a relationship between an amount of
displacement and an analysis error with respect to two types of
tile patterns having different white-to-black ratios. Here, a root
mean square (RMS) error of a difference between an analyzed amount
of displacement and a theoretical amount of displacement in an
evaluation area of 20.times.20 pixels at a center of the image.
[0068] It was confirmed that in the tile pattern with the
white-to-black ratio of 1:9, the noise reduction in the
conventional method was 14.9 .mu.m, whereas the noise reduction
according to the present invention was 4.1 .mu.m, and there is an
effect of noise reduction of 1/3 or more, as shown in FIG. 6.
[0069] It was confirmed that in the tile pattern with the
white-to-black ratio of 1:19, the analysis error in the
conventional method was 29.4 .mu.m, whereas the analysis error
according to the present invention was 7.2 .mu.m, which was 1/4 or
less of the analysis error in the conventional method, and the
precision could be improved.
[0070] From this simulation, it was confirmed that, for an
arbitrary regular pattern, by considering a plurality of higher
order frequency components, random noise could be greatly reduced,
and stable displacement measurement was performed with slight
variation.
[0071] FIG. 7 shows a relationship between orders of the frequency
used for analysis and a measurement error in the present invention.
It can be seen from this that it is possible to improve the
measurement precision by considering a plurality of frequency
components as compared with the conventional method that uses only
a component of frequency 1.
Example 3
Verification of Improvement of Displacement Distribution
Measurement Precision of One-Dimensional Regular Pattern Through
Experiment
[0072] FIG. 9 shows experimental results of displacement
distribution analysis using a tile pattern having one-dimensional
regularity using the optical system illustrated in FIG. 8 in order
to confirm effectiveness of the method described in the second
method (2) of the present invention.
[0073] In this experiment, an actual tile having a width of 95 mm
and a spacing of 5 mm was used. In this case, a white-to-black
ratio was 1:19, which was the same white-to-black ratio as that of
one tile pattern of the simulation in Example 2.
[0074] This tile was fixed onto a flat plate of a liner moving
stage, and an image capturing was performed using an optical camera
installed at a place separated from 4.5 m.
[0075] In this case, a grating pitch on a camera image was 40
pixels. The tile was moved in a horizontal direction by 0.1 mm step
from 0 mm to 2 mm from the moving stage, an image was captured at
each position (moving distance), and amounts of displacement in a
conventional method that uses only a first order frequency
component and the present invention that considers fundamental
frequency component and first to fifth order frequency components
were analyzed so as to calculate an average value of experimental
data in the evaluation area of 40.times.10 pixels at a center of
the image and a measurement error of an amount of the displacement
of the stage, and a standard deviation thereof.
[0076] FIG. 9(a) shows an average error obtained using the
conventional method and the present invention with respect to a
moving distance. It can be seen from this experimental result that,
according to the present invention, high-precision displacement
measurement was performed.
[0077] FIG. 9(b) shows a standard deviation of a measurement error
obtained using the conventional method and the present invention
with respect to the moving distance. It was possible to reduce to
less than a quarter of variation as compared with the conventional
method.
Example 4
Verification of Improvement of Displacement Distribution
Measurement Precision of Two-Dimensional Regular Pattern Through
Experiment
[0078] Experimental results of displacement distribution analysis
using a pattern having a two-dimensional regularity using an
optical system shown in FIG. 10 in order to confirm effectiveness
of the method described in the second method (2) of the present
invention are shown in FIG. 11.
[0079] In this experiment, three types of two-dimensional regular
patterns such as The letter "A", number "3", and Chinese character
"" having a pitch spacing of 10 mm in addition to the square wave
pattern used in a conventional method (for comparison with the
present invention) were used.
[0080] The four types of patterns were fixed onto the flat plate of
the linear moving stage, and image capturing was performed using an
optical camera installed at a place separated from 1350 mm.
[0081] In this case, a grating pitch on a camera image was 20
pixels. The pattern was moved in a horizontal direction by 0.02 mm
from 0 mm to 1 mm from the linear moving stage, and an image at
each position (a moving distance) was captured. Amounts of
displacement according to a conventional method that uses only a
first order frequency component and the present invention
considering the fundamental frequency component and first to fifth
order frequency components were analyzed respectively, and a root
mean square (RMS) of a measurement error of the experimental value
in an evaluation area of 20.times.20 pixels at a center of the
image and an amount of displacement of the stage was
calculated.
[0082] FIG. 11 shows an RMS error obtained using the conventional
method and the present invention with respect to the moving
distance. With any of three types of two-dimensional regular
patterns, significant improvement of the measurement precision was
achieved.
[0083] Specifically, in the case of the repetitive regular pattern
of number "3", the RMS average error of the conventional method was
26.3 .mu.m, whereas the RMS average error of the present invention
was 12.1 p.m. The measurement precision could be improved by 2.2
times.
[0084] In the case of the repetitive regular pattern of Chinese
character "*", the RMS average error of the conventional method was
76.6 .mu.m, whereas the RMS average error of the present invention
was 12.2 .mu.m. The measurement precision could be improved by 6.3
times.
[0085] In the case of a repetitive regular pattern of the letter
"A", the RMS average error of the conventional method was 112.4
.mu.m, whereas the RMS average error of the present invention was
10.0 .mu.m. The measurement precision could be improved by 11.2
times.
[0086] On the other hand, in the case of a rectangular wave pattern
used in the conventional method, the RMS average error of the
conventional method was 8.7 .mu.m, whereas the RMS average error of
the present invention was 9.6 .mu.m. The same degree of measurement
precision was achieved.
[0087] According to the present invention, with respect to any of
the three types of two-dimensional regular patterns used in this
experiment, the measurement of a small amount of displacement
distribution with the measurement precision of about 10 .mu.M was
achieved.
[0088] This is a surprisingly high measurement precision that is
indeed 1/1000 of 10 mm that is a pattern pitch. That is, if an
atomic arrangement pattern of a nano scale observed by an electron
microscope is analyzed, displacement distribution of sub-Angstrom
order that is smaller than atoms can be theoretically analyzed.
[0089] On the other hand, by regarding window glass of a high-rise
building arranged with spacings of one meter as a regular pattern
and analyzing the window glass, shaking or deflecting of the entire
building can be detected with precision of mm order only by
capturing the building using the optical camera from a
distance.
Example 5
[0090] In the above example, the program was produced using C
(programming language) and C.sup.++ (programming language) and each
displacement distribution measurement method was executed so as to
measure the displacement distribution.
[0091] The program language is not limited to C and C.sup.++, and
the program may be a program loaded into a RAM or may be a program
fixed in a ROM.
Example 6
[0092] In the above-described example, the image data obtained from
the optical camera was processed using a personal computer so as to
obtain a measurement result of each displacement distribution.
[0093] The displacement distribution measurement device may be
formed separately from the optical camera, or may be formed
integrally with the optical camera.
[0094] Further, the displacement distribution measurement device
may be incorporated in a displacement distribution analysis device,
or may be incorporated in various measurement devices by setting
appropriate input and output specifications and integration into
one chip of the displacement distribution measurement device.
INDUSTRIAL APPLICABILITY
[0095] Since the present invention can be applied to an arbitrary
regular pattern, the present invention is suitably applied to
evaluation of mechanical characteristics of a newly developed
material or diagnosis of health monitoring of an infrastructure.
Objects having wide range from a nano/micro scale to a mega scale
can be a analysis target of the present invention.
[0096] More specifically, industrial fields to which the present
invention can be applied and deployed may include fields of
nano-science, mechanical material, infrastructure civil
engineering, and biomimetics.
REFERENCE SIGNS LIST
[0097] 1 sample [0098] 2 load mechanism [0099] 3 support [0100] 4
enlarged view of grating pattern [0101] 5 camera [0102] 6
one-dimensional repetitive pattern [0103] 7 moving direction [0104]
8 linear moving stage
* * * * *